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Prs sts r sts t Pr r strt s t

  1. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐✯ ❛♥❞ ❈❛r♠✐♥❡ ❱❡♥tr❡ ❯♥✐✈❡rs✐tà ❞❡❣❧✐ ❙t✉❞✐ ❞✐ ❙❛❧❡r♥♦ ❯♥✐✈❡rs✐t② ♦❢ ▲✐✈❡r♣♦♦❧ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  2. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ▼♦❞❡❧ ✶ ✷ ❆ ✸ ❇ ♥ = ✺ , ♠ = ✸ ✹ ❈ ✺ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  3. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ▼♦❞❡❧ ✶ ✷ ❆ ✸ ❇ ♥ = ✺ , ♠ = ✸ ✹ ❈ ✺ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  4. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ▼♦❞❡❧ ✶ ✇ ✶ ❆ = ✺ ✇ ✷ ❆ = ✸✶ ✷ ❆ ✇ ✷ ❇ = ✷✸ ♥ = ✺ , ♠ = ✸ ✇ ✸ ❇ = ✺✺ ✸ ❇ ✇ ♠✐♥ = ✶ . ✺ ✇ ✸ ❈ = ✶ . ✺ ✇ ♠❛① = ✺✺ ✇ ✹ ❈ = ✷✹ s = ✇ ♠❛① ✺✺ ✹ ❈ ✇ ♠✐♥ = ✶ . ✺ ✼ = ✇ ❈ ✺ ✺ ❘❡str✐❝t❡❞ ❯♥r❡❧❛t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  5. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ▼♦❞❡❧ ✶ ✇ ✶ = ✹ ✷ ✇ ✷ = ✻ ❆ ✈ ❆ = ✷ ♥ = ✺ , ♠ = ✸ ✸ ❇ ✈ ❇ = ✼ ✇ ✐ ✇ ✸ = ✾ ✇ ✐❥ = ✈ ❥ r = ♠❛① ❥ ✈ ❥ ♠✐♥ ❥ ✈ ❥ = ✼ ✷ ✹ ❈ ✇ ✹ = ✺ ✈ ❈ = ✹ t = ♠❛① ✐ ✇ ✐ ♠✐♥ ✐ ✇ ✐ = ✾ ✶ ✺ ✇ ✺ = ✶ ❘❡str✐❝t❡❞ ❘❡❧❛t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  6. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ▼♦❞❡❧ ✶ ❥ ✶ = ❆ ✇ ✶ ❆ = ✺ ♥ ❆ = ✶ ✇ ✷ ❆ = ✸✶ ✷ ❥ ✷ = ❇ ❆ ❝ ❆ = ✺ ✇ ✷ ❇ = ✷✸ ♥ ❇ = ✶ ✇ ✸ ❇ = ✺✺ ❥ ✸ = ❈ ✸ ❇ ❝ ❇ = ✷✸ ✇ ✸ ❈ = ✶ . ✺ ✇ ✹ ❈ = ✷✹ ♥ ❈ = ✸ ✹ ❈ ❥ ✹ = ❈ ❝ ❈ = ✸✷ . ✺ ✼ = ✇ ❈ ✺ ✺ ❥ ✺ = ❈ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  7. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ❉❡✜♥✐t✐♦♥ ❉❡✜♥✐t✐♦♥ ❆♥ ❖♣t✐♠❛❧ ❙♦❧✉t✐♦♥ ✭ ❖P❚ ✮ ✐s ❛♥ ❛ss✐❣♥♠❡♥t t❤❛t ♠✐♥✐♠✐③❡ t❤❡ ♦❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ s❡❧❡❝t❡❞ ❜② t❤❡ ❞❡s✐❣♥❡r✳ ✭❊①✿ � ✐ ❝ ❥ ✐ ✮ ❥ ∗ ✶ ✶ = ❆ ✇ ✶ ❆ = ✺ ♥ ∗ ❆ = ✶ ✇ ✷ ❆ = ✸✶ ❥ ∗ ✷ = ❇ ✷ ❆ ❝ ∗ ❆ = ✺ ✇ ✷ ❇ = ✷✸ ♥ ∗ ❇ = ✶ ✇ ✸ ❇ = ✺✺ ❥ ∗ ✸ ❇ ✸ = ❈ ❝ ∗ ❇ = ✷✸ ✇ ✸ ❈ = ✶ . ✺ ♥ ∗ ❈ = ✸ ✇ ✹ ❈ = ✷✹ ❥ ∗ ✹ ✹ = ❈ ❈ ❝ ∗ ❈ = ✸✷ . ✺ ✼ = ✇ ❈ ✺ ❥ ∗ ✺ = ❈ ✺ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  8. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts ❉❡✜♥✐t✐♦♥ ❉❡✜♥✐t✐♦♥ ❆ ◆❛s❤ ❊q✉✐❧✐❜r✐✉♠ ❙♦❧✉t✐♦♥ ✭ ◆❆❙❍ ✮ ✐s ❛♥ ❛ss✐❣♥♠❡♥t ✇❤❡r❡ ♥♦ ❥♦❜ ❝❛♥ ✉♥✐❧❛t❡r❛❧❧② ✐♠♣r♦✈❡ ✐ts ❧❛t❡♥❝② ♠♦✈✐♥❣ t♦ ❛♥♦t❤❡r ♠❛❝❤✐♥❡✳ ∀ ❥♦❜ ✐ , ∀ ♠❛❝❤✐♥❡ ❥ , ❝ ❥ ✐ ≤ ❝ ❥ + ✇ ✐❥ . ❥ ✶ = ❆ ✶ ✇ ✶ ❆ = ✺ ♥ ❆ = ✶ ✇ ✷ ❆ = ✸✶ ✷ ❆ ❥ ✷ = ❇ ❝ ❆ = ✺ ✇ ✷ ❇ = ✷✸ ✇ ✸ ❇ = ✺✺ ♥ ❇ = ✶ ✸ ❇ ❥ ✸ = ❈ ❝ ❇ = ✷✸ ✇ ✸ ❈ = ✶ . ✺ ♥ ❈ = ✸ ✇ ✹ ❈ = ✷✹ ❥ ✹ = ❈ ✹ ❈ ❝ ❈ = ✸✷ . ✺ ✼ = ✇ ✺ ❈ ✺ ❥ ✺ = ❈ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  9. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ❉❡✜♥✐t✐♦♥ ❚❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ✭ P♦❆ ✮ ❬❑P✾✾❪ ✐s t❤❡ r❛t✐♦ ❜❡t✇❡❡♥ t❤❡ ❝♦st ♦❢ t❤❡ ✇♦rst ◆❛s❤ ❊q✉✐❧✐❜r✐✉♠ ❙♦❧✉t✐♦♥ ❛♥❞ t❤❡ ❝♦st ♦❢ t❤❡ ❖♣t✐♠❛❧ ❙♦❧✉t✐♦♥✳ P♦❆ = ❈ ( ◆❆❙❍ ) ❈ ( ❖P❚ ) ■t ♠❡❛s✉r❡s ❤♦✇ ♠✉❝❤ t❤❡ ❧❛❝❦ ♦❢ ❝❡♥tr❛❧ ❝♦♦r❞✐♥❛t✐♦♥ ❝❛♥ ❛✛❡❝t t❤❡ s②st❡♠✳ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  10. ▼♦❞❡❧ Pr❡✈✐♦✉s ❘❡s✉❧ts ❖✉r ❘❡s✉❧ts Pr❡✈✐♦✉s ❘❡s✉❧ts ❊①✐st❡♥❝❡ ❆ ◆❛s❤ ❊q✉✐❧✐❜r✐✉♠ ❙♦❧✉t✐♦♥ ❛❧✇❛②s ❡①✐sts✳ ❬❊❞❑▼✵✸❪ ▼❛①✐♠✉♠ ▲❛t❡♥❝② ( ♠✐♥ ♠❛① ❥ ❝ ❥ ) � � ❧♦❣ ♠ P♦❆ = Θ s + ✐♥ t❤❡ ❯♥r❡❧❛t❡❞ ❙❡tt✐♥❣❀ ❬❆❆❘❚✵✸❪ ❧♦❣ ( ✶ + ❧♦❣ ♠ ) s � � ❧♦❣ ♠ P♦❆ = Θ ✐♥ ❘❡❧❛t❡❞ ❙❡tt✐♥❣✳ ❬❆❆❘❚✵✸❪ ❧♦❣ ❧♦❣ ♠ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  11. ▼♦❞❡❧ ❙❡r✈❡r ▲❛t❡♥❝② Pr❡✈✐♦✉s ❘❡s✉❧ts ❚♦t❛❧ ▲❛t❡♥❝② ❖✉r ❘❡s✉❧ts ❲❡✐❣❤t❡❞ ❚♦t❛❧ ▲❛t❡♥❝② ❖✉r ❘❡s✉❧ts ❇♦✉♥❞s ♦♥ P♦❆ ❢♦r ❙❡r✈❡r ▲❛t❡♥❝②❀ ❚♦t❛❧ ▲❛t❡♥❝②❀ ❲❡✐❣❤t❡❞ ❚♦t❛❧ ▲❛t❡♥❝②✳ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  12. ▼♦❞❡❧ ❙❡r✈❡r ▲❛t❡♥❝② Pr❡✈✐♦✉s ❘❡s✉❧ts ❚♦t❛❧ ▲❛t❡♥❝② ❖✉r ❘❡s✉❧ts ❲❡✐❣❤t❡❞ ❚♦t❛❧ ▲❛t❡♥❝② ❙❡r✈❡r ▲❛t❡♥❝② ❉❡✜♥✐t✐♦♥ ❚❤✐s ♦❜❥❡❝t✐✈❡ ❢✉♥❝t✐♦♥ ♠✐♥✐♠✐③❡s t❤❡ t♦t❛❧ ❧♦❛❞ s✉✛❡r❡❞ ❜② t❤❡ ♠❛❝❤✐♥❡s✳ ♠✐♥ � ❥ ❝ ❥ = ♠✐♥ � ✐ ✇ ✐❥ ✐ ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

  13. ▼♦❞❡❧ ❙❡r✈❡r ▲❛t❡♥❝② Pr❡✈✐♦✉s ❘❡s✉❧ts ❚♦t❛❧ ▲❛t❡♥❝② ❖✉r ❘❡s✉❧ts ❲❡✐❣❤t❡❞ ❚♦t❛❧ ▲❛t❡♥❝② ❙❡r✈❡r ▲❛t❡♥❝② ✲ ✷ ❖✉r ❘❡s✉❧t ✲ ❯♥r❡❧❛t❡❞ ❙❡tt✐♥❣ P♦❆ = Θ ( s ) ❖✉r ❘❡s✉❧t ✲ ❘❡❧❛t❡❞ ❙❡tt✐♥❣ P♦❆ = Θ ( ♠✐♥ ( r , ♥ )) ❉✐♦❞❛t♦ ❋❡rr❛✐♦❧✐ ❖♥ t❤❡ Pr✐❝❡ ♦❢ ❆♥❛r❝❤② ♦❢ ❘❡str✐❝t❡❞ ❏♦❜ ❙❝❤❡❞✉❧✐♥❣ ●❛♠❡s

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